Of course I know what the KfW standards are and what you have to prove for them. Controlled residential ventilation only makes sense together with insulation so that it is not like a thermos flask, including mold due to insufficient active window ventilation.
For me, the question is whether it makes sense to apply the insulation and controlled residential ventilation (decentralized) already now during the renovation, or if you can wait with that. I have to take a look at the energy consumption of recent years.
Regarding the inspection with a specialist, basically everything has already been said, and I can only support that. Regarding the issue of insulation, please do not believe everything some expert colleague says on television (especially not the one who always appears when insulation is discussed). Assuming the insulation is properly planned and installed, you will not get mold problems. Because the wall will not cool down so much and therefore will not become so cold inside that moisture condenses on the wall. Thus, insulation of the exterior wall surfaces prevents mold formation. Because without moisture, there is no mold.
Honestly, the current state is much more problematic; the house has new windows installed and the walls are uninsulated. Therefore, the walls are now less insulated than the windows. To avoid mold, it should be exactly the other way around so that any possible condensate forms on the window and not on the wall. Because on the walls there are many organic materials like wallpaper, adhesive, additives in the plaster, and possibly house dust. Mold needs moisture and food (organic materials) to grow.
However, if you apply regular ETICS with the very thin plaster layer, your house will become unsightly more quickly due to algae growth. Because the thin plaster layer cools down quickly and also gets sufficiently moist quickly enough to support algae growth. Thicker plaster layers are an improvement here.
Everything I have tried to explain to you, you actually know anyway and can easily confirm through an experiment. Go to the refrigerator and get a bottle of beer. Place a second bottle next to it that is at room temperature. What happens? The cold bottle gets wet. Exactly the same happens with your wall.
Since we live in Germany, mold formation is also standardized in 4108 Thermal insulation in building construction. Conditions: Outside -5°C, inside +20°C, indoor humidity 50%, wall surface temperature 12.6°C, mold then develops.
Therefore, my recommendation is to insulate immediately!